- Email: [email protected]
Self and transport diffusion of fluids in SiO2 alcogels studied by NMR pulsed gradient spin echo and NMR imaging
Journal of Non-Crystalline Solids 225 Ž1998. 91–95
Self and transport diffusion of fluids in SiO 2 alcogels studied by NMR pulsed gradient spin echo and NMR imaging W. Behr b
a,)
, A. Haase a , G. Reichenauer b, J. Fricke
a
a Physikalisches Institut der UniÕersitat Am Hubland, 97074 Wurzburg, Germany ¨ Wurzburg, ¨ ¨ Bayerisches Zentrum fur Germany ¨ Angewandte Energieforschung, Am Hubland, 97074 Wurzburg, ¨
Abstract Preparation of SiO 2 aerogels generally includes a fluid exchange step either to chemically modify the material or to allow an optimized drying of the alcogel. As the degree of fluid already exchanged affects the properties of the resulting aerogel or xerogel and the fluid replacement is a time consuming process, it is a big advantage if the exchange rate can be predicted for a certain type of gel. An autoclave for pressures up to 10 MPa and temperatures up to 808C, that can be used as probehead for a standard NMR system, has been designed. This device allows in situ pulsed gradient spin echo ŽPGSE. and NMR imaging. Self diffusion coefficients for methanol in TMOS gels of different nanostructure have been determined by PGSE. NMR imaging was applied to observe online the fluid exchange of methanol for liquid CO 2 at a pressure of about 7 MPa at 158C. Alcogel structures have been investigated by small angle X-ray scattering ŽSAXS.. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Self and transport diffusion; SiO 2 alcogels; NMR imaging
1. Introduction The production of silica aerogels requires several steps. After the gelation, the pore volume of the alcogel is filled with the reaction fluid, mostly methanol. Prior to low temperature supercritical drying, this fluid has to be exchanged for liquid CO 2 . The fluid exchange step is a time consuming process. Although some work has been done to study the exchange kinetics w1x, up to now no in situ measurements were possible.
)
Corresponding author. Tel.: q49-931 888 5749; fax: q49-931 888 5158; e-mail: [email protected].
Silica aerogels as well as their alcogel precursors consist of a three-dimensional open porous nanostructured network, that can be described in terms of fractals w2,3x. The parameters that characterize the fractal structure, i.e., the upper and lower limit of the fractal range and the fractal dimension depend on the sample density and the catalyst used in the sol–gel process, respectively. These quantities can be determined by small-angle X-ray scattering ŽSAXS.; however, SAXS data do not provide direct information about the connectivity of the pores, which is relevant for the fluid transport. The objective of this work is therefore to investigate both, the structure and the fluid transport within the pores of silica alcogels prepared under different conditions by SAXS and NMR.
0022-3093r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 3 0 9 3 Ž 9 8 . 0 0 0 1 2 - X
W. Behr et al.r Journal of Non-Crystalline Solids 225 (1998) 91–95
92
2. Theoretical background
3. Experimental procedure
Self diffusion is the motion of particles or molecules when no concentration gradient is present, whereas, transport diffusion requires a concentration gradient. However, self diffusion and transport via molecular diffusion in a porous matrix like an alcogel have one point in common: they are slowed by the same factor compared to either self diffusion or molecular transport in the free fluid w4x. The relevant quantities for the slowing of diffusional motion in fractal structures are the upper and lower limit of the fractal range Ž j and R, see Eq. Ž1.. as well as the fractal dimension D w5x. The fractality of a sample shows in SAXS patterns as a scaling law of the scattered intensity I as a function of wave vector q:
Three sets of tetrametoxysilane ŽTMOS.-alcogels were prepared with a fixed molar ratio of H 2 O to TMOS of 4:1 under basic ŽB., neutral ŽN. and acidic ŽA. conditions. Each series consists of three samples with different target density, i.e., 80, 140 and 200 kgrm3. The catalysts used for acid and base-catalyzed gels were HCl and NH 4 OH. For 40 ml of an alcogel with a target density of 140 kgrm3 prepared under acidic conditions ŽA140. 14.20 g of TMOS were diluted in 15.03 g MeOH. Subsequently, 6.33 g water were added while stirring the solution. Finally, 0.39 g 0.01 nHCl were slowly added to the solution. For SAXS analysis, a small amount of the as prepared sol was soaked into a glass capillary of about 1 mm in diameter and 10 cm in length. Both ends then have been sealed by melting the glass. The length of the sol in the center of the capillary was about 1 to 2 cm. For NMR investigations, glass cylinders with an inner diameter of 14 mm and a height of 10 cm were filled with the same sol and sealed to avoid evaporation of the solvent. Depending on target density and catalyst the sol gelled within hours up to 1 week at 308C. Subsequently, all gels were aged for 4 weeks at 308C. SAXS was performed at the German synchrotron source at DESYr Hamburg. The NMR-measurements were performed at a Bruker–Biospec with a horizontal magnetic field of 7 T. For the imaging of the fluid exchange, an NMR-suitable autoclave has been built that satisfies the following requirements: non-magnetic, max. operating pressure 10 MPa, adjustable temperature range Ž108C . . . 358C., ‘invisible’ for HF-fields Žno induction of eddy currents. and chemically stable with respect to supercritical CO 2 . The cell body, a hollow cylinder made of the thermoplastic PEEK Žpoly–ether–ether–ketone. with an inner diameter of 28 mm, is sealed off at both ends by detachable brass caps, one of them is easily accessible for sample change, the other one contains fluid inlet and outlet capillaries ŽFig. 1.. As for a standard low temperature supercritical drying procedure, the alcogel was removed from the PE-moulds and placed in a transfer boat before the residual volume was filled with methanol and the probehead could be closed. The transfer boat constructed for our NMR-autoclave has
I ; qyD for j ) 1rq ) R.
Ž 1.
j is the size of the fractal clusters and R is the radius of a primary particle. The exact scattering structure factor for fractal aggregates is given in Ref. w6x. NMR is based on the interaction between an external magnetic field and a nucleus with a nonvanishing spin. In an NMR-measurement a high frequency field applied to the sample causes a signal which can be detected by an radio frequency coil. The signal amplitude depends on the amount of protons and also on some NMR-relevant parameters like the surrounding of the protons and the homogeneity of the magnetic field. By applying magnetic field gradients during the RF-pulse slices of a specimen can be selected for NMR imaging. Within this frame, NMR imaging yields a two-dimensional concentration profile of the protons in the material under investigation. Using the pulsed gradient spin echo sequence w7x with well-defined time delays and gradients applied between the pulses, the self diffusion coefficient D S of fluids in alcogels can be determined via
ž
A Ž g . s A 0 exp yg 2d 2 g 2 D y
ž
1 3
/ /
d DS ,
Ž 2.
where A and A 0 are the echo amplitudes of the NMR signal as a function of applied gradient g and for g s 0, respectively, g is the gyromagnetic ratio of the nucleus, d is the duration of the gradient with the strength g and D the diffusion time.
W. Behr et al.r Journal of Non-Crystalline Solids 225 (1998) 91–95
93
Fig. 1. Cross-section of the self-designed and self-built NMR probehead that is suited for operating pressures up to 10 MPa and temperatures up to 808C.
the same features as the ones for commercial autoclaves. Alcogels with diameters up to 14 mm and a length up to 100 mm can be easily handled. The temperature of the pressure cell which is adjustable with a water Žor air. flow controlled by a thermostat connected to a tube surrounding the PEEK cylinder. The set-up allows pressure- and CO 2-flow-control by two adjustable valves, a high pressure transducer and a flow meter. Self diffusion coefficients were determined at room temperature for three series of gels prepared with different catalyst. Diffusional transport coefficient in the neutrally reacted sample with a target density of 80 kgrm3 was also investigated by NMR imaging. Using the special NMR-pulse sequence FLASH such an image can be obtained within seconds w8x. During NMR imaging of the fluid exchange process the pressure cell was held at a temperature of 158C. After a fast exchange of the methanol around the sample for liquid CO 2 within 3 min, a continuous flow of liquid CO 2 was applied and the MeOH concentration profile in the alcogel was recorded in steps of 15 min.
that takes into account a lower and upper cutoff of the fractal scaling regime ŽEq. Ž1.., the packing of the fractal clusters, scattering from smooth primary particles surfaces and a linear background that affects the scattering curve only at the high q end of the experimental range w6x. The fits yield primary particle radii of Ž0.3 " 0.1. nm, Ž1.3 " 0.1. nm and Ž1.9 " 0.1. nm for the acid, the neutrally and the base-catalyzed alcogels, respectively. The fractal dimensions deduced are D s 2.2 " 0.1 ŽA., 2.1 " 0.1 ŽN. and 2.3 " 0.1 ŽB.. The self diffusion coefficient D S for MeOH in alcogels prepared with different catalysts and target densities determined via Eq. Ž2. are plotted vs. porosity in Fig. 3.
4. Results SAXS data for samples prepared with different catalysts as well as for base-catalyzed TMOS gels with different target densities are depicted in Fig. 2. The small intermediate scaling ranges, especially for samples with higher target density, indicate that the alcogels investigated are far from being ‘perfect fractals’; therefore, the datasets were fitted in the complete experimental q-range by a structure factor
Fig. 2. Ža. SAXS data for TMOS alcogels with a target density of 80 kgrm3 prepared under acidic ŽA., basic ŽB. and neutrally ŽN. conditions. Žb. SAXS data for base-catalyzed alcogels with target densities of 80, 140 and 200 kgrm3. The curves are arbitrarily shifted relative to each other for better visibility.
94
W. Behr et al.r Journal of Non-Crystalline Solids 225 (1998) 91–95
5. Discussion
Fig. 3. Self diffusion coefficient D S of methanol in TMOS alcogels with different porosities Ž1y r T r r S . prepared under basic ŽB., neutral ŽN. and acidic ŽA. conditions. The self diffusion coefficient for free methanol is given as the limiting value for porosity equal to one.
Some of the NMR images recorded during the fluid exchange methanolrCO2 in a neutral-catalyzed TMOS-gel with a target density of 80 kgrm3 are shown in Fig. 4. Solving the diffusion equation for the cylindrical geometry of the alcogel with radius a and given initial and boundary conditions for the CO 2 concentration CCO 2 w9x, i.e., CCO 2 s 0 for t s 0 and r F a and CCO 2 s const. for r ) a
Ž 3.
a transport diffusion coefficient D T s Ž0.9 " 0.2. P 10y9 m2rs was determined from the concentration profile taken after 120 min.
The self diffusion coefficients for methanol in TMOS alcogels, as expected, reveal a significant decrease with decreasing porosity Ž1 y r Trr S ., with r T , the target density of the alcogels and r S s 2200 kgrm3, the density of silica ŽFig. 3.. Furthermore, at a given porosity, D S is smaller for acid compared to base catalyzed alcogels. This can be understood in terms of a slower diffusional motion in a branched polymerlike network Žalcogels A. than in a gel with a colloidal substructure ŽB. at the same porosity. The ratio of the self diffusion coefficients for free methanol to methanol in the base-catalyzed alcogels ranges from 1.3 to 1.7. This is close to the average tortuosity t s 1.9 determined from gas diffusion studies of base-catalyzed silica aerogels w10x, which is reasonable as the tortuosity should be the major slowing factor in both experiments. The transport diffusion coefficient determined for MeOH in liquid CO 2 at a pressure of 7 MPa within a neutrally reacted alcogel Žtarget density 80 kgrm3 . is D T s Ž0.9 " 0.2. = 10y9 m2rs. This value is significantly lower than the self diffusion coefficient of pure methanol at ambient conditions in the same sample which is D S s 2.26 = 10y9 m2rs. This can be attributed to the fact that mobility of a molecule decreases with increasing pressure and can strongly vary with the solvent w11x, in our case, the CO 2rmethanol concentration. In addition, one has to keep in mind that the NMR signal is not only a function of the proton concentration but depends also
Fig. 4. NMR cross-sectional images of the neutrally-catalyzed alcogel with a target density of 80 kgrm3 as a function of time showing the online fluid exchange of methanol for liquid CO 2 .
W. Behr et al.r Journal of Non-Crystalline Solids 225 (1998) 91–95
on the spin–spin and spin–lattice relaxation times. These quantities are known to be affected in a very complex manner by the kinetics in the system under investigation w12x. Further experiments are therefore necessary to identify or exclude relaxation times effects and to investigate the influence of pressure and solvent concentration on the diffusion coefficient of methanol in silica alcogels.
6. Conclusion We have presented first results on the transport diffusion in silica alcogels derived via new technique for online imaging of the fluid exchange under high pressure. Studies of the self diffusion coefficients via NMR–PGSE are a fast tool to achieve information about transport in silica alcogels.
Acknowledgements This work has been funded by the German Research Foundation ŽDFG..
95
References w1x G. Rogacki, P. Wawrzyniak, J. Non-Cryst. Solids 186 Ž1995. 73. w2x R. Vacher, T. Woignier, J. Phalippou, J. Pelous, E. Courtens, Rev. Phys. Appl. C 4 Ž1989. 127. w3x D.W. Schaefer, Rev. Phys. Appl. C 4 Ž1989. 121. w4x W.P. Pollard, R.D. Present, Phys. Rev. 73 Ž1948. 762. w5x Y. Glen, A. Aharony, S. Alexander, Phys. Rev. Lett. 50 Ž1973. 77. w6x A. Emmerling, P. Wang, G. Popp, A. Beck, J. Fricke, J. Phys. IV C 8 Ž3. Ž1993. 357. w7x E.O. Stejskal, J.E. Tanner, J. Chem. Phys. 42 Ž1965. 288. w8x A. Haase, Magn. Reson. Med. 13 Ž1990. 77. w9x H.S. Carslow, J.C. Jaeger, Conduction of Heats in Solids, Clarendon, Oxford, 1995. w10x G. Reichenauer, C. Stumpf, J. Fricke, J. Non-Cryst. Solids 186 Ž1995. 334. w11x R.C. Weast, M.J. Astle, W.H. Beyer, CRC Handbook of Chemistry and Physics, CRC, Boca Raton, FL, 1985. w12x C.N. Chen, D.I. Hoult, Biomedical Magnetic Resonance Technology, Adam Hilger, Bristol, 1989.
Self and transport diffusion of fluids in SiO 2 alcogels studied by NMR pulsed gradient spin echo and NMR imaging W. Behr b
a,)
, A. Haase a , G. Reichenauer b, J. Fricke
a
a Physikalisches Institut der UniÕersitat Am Hubland, 97074 Wurzburg, Germany ¨ Wurzburg, ¨ ¨ Bayerisches Zentrum fur Germany ¨ Angewandte Energieforschung, Am Hubland, 97074 Wurzburg, ¨
Abstract Preparation of SiO 2 aerogels generally includes a fluid exchange step either to chemically modify the material or to allow an optimized drying of the alcogel. As the degree of fluid already exchanged affects the properties of the resulting aerogel or xerogel and the fluid replacement is a time consuming process, it is a big advantage if the exchange rate can be predicted for a certain type of gel. An autoclave for pressures up to 10 MPa and temperatures up to 808C, that can be used as probehead for a standard NMR system, has been designed. This device allows in situ pulsed gradient spin echo ŽPGSE. and NMR imaging. Self diffusion coefficients for methanol in TMOS gels of different nanostructure have been determined by PGSE. NMR imaging was applied to observe online the fluid exchange of methanol for liquid CO 2 at a pressure of about 7 MPa at 158C. Alcogel structures have been investigated by small angle X-ray scattering ŽSAXS.. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Self and transport diffusion; SiO 2 alcogels; NMR imaging
1. Introduction The production of silica aerogels requires several steps. After the gelation, the pore volume of the alcogel is filled with the reaction fluid, mostly methanol. Prior to low temperature supercritical drying, this fluid has to be exchanged for liquid CO 2 . The fluid exchange step is a time consuming process. Although some work has been done to study the exchange kinetics w1x, up to now no in situ measurements were possible.
)
Corresponding author. Tel.: q49-931 888 5749; fax: q49-931 888 5158; e-mail: [email protected].
Silica aerogels as well as their alcogel precursors consist of a three-dimensional open porous nanostructured network, that can be described in terms of fractals w2,3x. The parameters that characterize the fractal structure, i.e., the upper and lower limit of the fractal range and the fractal dimension depend on the sample density and the catalyst used in the sol–gel process, respectively. These quantities can be determined by small-angle X-ray scattering ŽSAXS.; however, SAXS data do not provide direct information about the connectivity of the pores, which is relevant for the fluid transport. The objective of this work is therefore to investigate both, the structure and the fluid transport within the pores of silica alcogels prepared under different conditions by SAXS and NMR.
0022-3093r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 3 0 9 3 Ž 9 8 . 0 0 0 1 2 - X
W. Behr et al.r Journal of Non-Crystalline Solids 225 (1998) 91–95
92
2. Theoretical background
3. Experimental procedure
Self diffusion is the motion of particles or molecules when no concentration gradient is present, whereas, transport diffusion requires a concentration gradient. However, self diffusion and transport via molecular diffusion in a porous matrix like an alcogel have one point in common: they are slowed by the same factor compared to either self diffusion or molecular transport in the free fluid w4x. The relevant quantities for the slowing of diffusional motion in fractal structures are the upper and lower limit of the fractal range Ž j and R, see Eq. Ž1.. as well as the fractal dimension D w5x. The fractality of a sample shows in SAXS patterns as a scaling law of the scattered intensity I as a function of wave vector q:
Three sets of tetrametoxysilane ŽTMOS.-alcogels were prepared with a fixed molar ratio of H 2 O to TMOS of 4:1 under basic ŽB., neutral ŽN. and acidic ŽA. conditions. Each series consists of three samples with different target density, i.e., 80, 140 and 200 kgrm3. The catalysts used for acid and base-catalyzed gels were HCl and NH 4 OH. For 40 ml of an alcogel with a target density of 140 kgrm3 prepared under acidic conditions ŽA140. 14.20 g of TMOS were diluted in 15.03 g MeOH. Subsequently, 6.33 g water were added while stirring the solution. Finally, 0.39 g 0.01 nHCl were slowly added to the solution. For SAXS analysis, a small amount of the as prepared sol was soaked into a glass capillary of about 1 mm in diameter and 10 cm in length. Both ends then have been sealed by melting the glass. The length of the sol in the center of the capillary was about 1 to 2 cm. For NMR investigations, glass cylinders with an inner diameter of 14 mm and a height of 10 cm were filled with the same sol and sealed to avoid evaporation of the solvent. Depending on target density and catalyst the sol gelled within hours up to 1 week at 308C. Subsequently, all gels were aged for 4 weeks at 308C. SAXS was performed at the German synchrotron source at DESYr Hamburg. The NMR-measurements were performed at a Bruker–Biospec with a horizontal magnetic field of 7 T. For the imaging of the fluid exchange, an NMR-suitable autoclave has been built that satisfies the following requirements: non-magnetic, max. operating pressure 10 MPa, adjustable temperature range Ž108C . . . 358C., ‘invisible’ for HF-fields Žno induction of eddy currents. and chemically stable with respect to supercritical CO 2 . The cell body, a hollow cylinder made of the thermoplastic PEEK Žpoly–ether–ether–ketone. with an inner diameter of 28 mm, is sealed off at both ends by detachable brass caps, one of them is easily accessible for sample change, the other one contains fluid inlet and outlet capillaries ŽFig. 1.. As for a standard low temperature supercritical drying procedure, the alcogel was removed from the PE-moulds and placed in a transfer boat before the residual volume was filled with methanol and the probehead could be closed. The transfer boat constructed for our NMR-autoclave has
I ; qyD for j ) 1rq ) R.
Ž 1.
j is the size of the fractal clusters and R is the radius of a primary particle. The exact scattering structure factor for fractal aggregates is given in Ref. w6x. NMR is based on the interaction between an external magnetic field and a nucleus with a nonvanishing spin. In an NMR-measurement a high frequency field applied to the sample causes a signal which can be detected by an radio frequency coil. The signal amplitude depends on the amount of protons and also on some NMR-relevant parameters like the surrounding of the protons and the homogeneity of the magnetic field. By applying magnetic field gradients during the RF-pulse slices of a specimen can be selected for NMR imaging. Within this frame, NMR imaging yields a two-dimensional concentration profile of the protons in the material under investigation. Using the pulsed gradient spin echo sequence w7x with well-defined time delays and gradients applied between the pulses, the self diffusion coefficient D S of fluids in alcogels can be determined via
ž
A Ž g . s A 0 exp yg 2d 2 g 2 D y
ž
1 3
/ /
d DS ,
Ž 2.
where A and A 0 are the echo amplitudes of the NMR signal as a function of applied gradient g and for g s 0, respectively, g is the gyromagnetic ratio of the nucleus, d is the duration of the gradient with the strength g and D the diffusion time.
W. Behr et al.r Journal of Non-Crystalline Solids 225 (1998) 91–95
93
Fig. 1. Cross-section of the self-designed and self-built NMR probehead that is suited for operating pressures up to 10 MPa and temperatures up to 808C.
the same features as the ones for commercial autoclaves. Alcogels with diameters up to 14 mm and a length up to 100 mm can be easily handled. The temperature of the pressure cell which is adjustable with a water Žor air. flow controlled by a thermostat connected to a tube surrounding the PEEK cylinder. The set-up allows pressure- and CO 2-flow-control by two adjustable valves, a high pressure transducer and a flow meter. Self diffusion coefficients were determined at room temperature for three series of gels prepared with different catalyst. Diffusional transport coefficient in the neutrally reacted sample with a target density of 80 kgrm3 was also investigated by NMR imaging. Using the special NMR-pulse sequence FLASH such an image can be obtained within seconds w8x. During NMR imaging of the fluid exchange process the pressure cell was held at a temperature of 158C. After a fast exchange of the methanol around the sample for liquid CO 2 within 3 min, a continuous flow of liquid CO 2 was applied and the MeOH concentration profile in the alcogel was recorded in steps of 15 min.
that takes into account a lower and upper cutoff of the fractal scaling regime ŽEq. Ž1.., the packing of the fractal clusters, scattering from smooth primary particles surfaces and a linear background that affects the scattering curve only at the high q end of the experimental range w6x. The fits yield primary particle radii of Ž0.3 " 0.1. nm, Ž1.3 " 0.1. nm and Ž1.9 " 0.1. nm for the acid, the neutrally and the base-catalyzed alcogels, respectively. The fractal dimensions deduced are D s 2.2 " 0.1 ŽA., 2.1 " 0.1 ŽN. and 2.3 " 0.1 ŽB.. The self diffusion coefficient D S for MeOH in alcogels prepared with different catalysts and target densities determined via Eq. Ž2. are plotted vs. porosity in Fig. 3.
4. Results SAXS data for samples prepared with different catalysts as well as for base-catalyzed TMOS gels with different target densities are depicted in Fig. 2. The small intermediate scaling ranges, especially for samples with higher target density, indicate that the alcogels investigated are far from being ‘perfect fractals’; therefore, the datasets were fitted in the complete experimental q-range by a structure factor
Fig. 2. Ža. SAXS data for TMOS alcogels with a target density of 80 kgrm3 prepared under acidic ŽA., basic ŽB. and neutrally ŽN. conditions. Žb. SAXS data for base-catalyzed alcogels with target densities of 80, 140 and 200 kgrm3. The curves are arbitrarily shifted relative to each other for better visibility.
94
W. Behr et al.r Journal of Non-Crystalline Solids 225 (1998) 91–95
5. Discussion
Fig. 3. Self diffusion coefficient D S of methanol in TMOS alcogels with different porosities Ž1y r T r r S . prepared under basic ŽB., neutral ŽN. and acidic ŽA. conditions. The self diffusion coefficient for free methanol is given as the limiting value for porosity equal to one.
Some of the NMR images recorded during the fluid exchange methanolrCO2 in a neutral-catalyzed TMOS-gel with a target density of 80 kgrm3 are shown in Fig. 4. Solving the diffusion equation for the cylindrical geometry of the alcogel with radius a and given initial and boundary conditions for the CO 2 concentration CCO 2 w9x, i.e., CCO 2 s 0 for t s 0 and r F a and CCO 2 s const. for r ) a
Ž 3.
a transport diffusion coefficient D T s Ž0.9 " 0.2. P 10y9 m2rs was determined from the concentration profile taken after 120 min.
The self diffusion coefficients for methanol in TMOS alcogels, as expected, reveal a significant decrease with decreasing porosity Ž1 y r Trr S ., with r T , the target density of the alcogels and r S s 2200 kgrm3, the density of silica ŽFig. 3.. Furthermore, at a given porosity, D S is smaller for acid compared to base catalyzed alcogels. This can be understood in terms of a slower diffusional motion in a branched polymerlike network Žalcogels A. than in a gel with a colloidal substructure ŽB. at the same porosity. The ratio of the self diffusion coefficients for free methanol to methanol in the base-catalyzed alcogels ranges from 1.3 to 1.7. This is close to the average tortuosity t s 1.9 determined from gas diffusion studies of base-catalyzed silica aerogels w10x, which is reasonable as the tortuosity should be the major slowing factor in both experiments. The transport diffusion coefficient determined for MeOH in liquid CO 2 at a pressure of 7 MPa within a neutrally reacted alcogel Žtarget density 80 kgrm3 . is D T s Ž0.9 " 0.2. = 10y9 m2rs. This value is significantly lower than the self diffusion coefficient of pure methanol at ambient conditions in the same sample which is D S s 2.26 = 10y9 m2rs. This can be attributed to the fact that mobility of a molecule decreases with increasing pressure and can strongly vary with the solvent w11x, in our case, the CO 2rmethanol concentration. In addition, one has to keep in mind that the NMR signal is not only a function of the proton concentration but depends also
Fig. 4. NMR cross-sectional images of the neutrally-catalyzed alcogel with a target density of 80 kgrm3 as a function of time showing the online fluid exchange of methanol for liquid CO 2 .
W. Behr et al.r Journal of Non-Crystalline Solids 225 (1998) 91–95
on the spin–spin and spin–lattice relaxation times. These quantities are known to be affected in a very complex manner by the kinetics in the system under investigation w12x. Further experiments are therefore necessary to identify or exclude relaxation times effects and to investigate the influence of pressure and solvent concentration on the diffusion coefficient of methanol in silica alcogels.
6. Conclusion We have presented first results on the transport diffusion in silica alcogels derived via new technique for online imaging of the fluid exchange under high pressure. Studies of the self diffusion coefficients via NMR–PGSE are a fast tool to achieve information about transport in silica alcogels.
Acknowledgements This work has been funded by the German Research Foundation ŽDFG..
95
References w1x G. Rogacki, P. Wawrzyniak, J. Non-Cryst. Solids 186 Ž1995. 73. w2x R. Vacher, T. Woignier, J. Phalippou, J. Pelous, E. Courtens, Rev. Phys. Appl. C 4 Ž1989. 127. w3x D.W. Schaefer, Rev. Phys. Appl. C 4 Ž1989. 121. w4x W.P. Pollard, R.D. Present, Phys. Rev. 73 Ž1948. 762. w5x Y. Glen, A. Aharony, S. Alexander, Phys. Rev. Lett. 50 Ž1973. 77. w6x A. Emmerling, P. Wang, G. Popp, A. Beck, J. Fricke, J. Phys. IV C 8 Ž3. Ž1993. 357. w7x E.O. Stejskal, J.E. Tanner, J. Chem. Phys. 42 Ž1965. 288. w8x A. Haase, Magn. Reson. Med. 13 Ž1990. 77. w9x H.S. Carslow, J.C. Jaeger, Conduction of Heats in Solids, Clarendon, Oxford, 1995. w10x G. Reichenauer, C. Stumpf, J. Fricke, J. Non-Cryst. Solids 186 Ž1995. 334. w11x R.C. Weast, M.J. Astle, W.H. Beyer, CRC Handbook of Chemistry and Physics, CRC, Boca Raton, FL, 1985. w12x C.N. Chen, D.I. Hoult, Biomedical Magnetic Resonance Technology, Adam Hilger, Bristol, 1989.